MathDB

Let

1+x+x^2+...+x^{n-1}=F(x)G(x)

, where

n>1

and where

F

and

G

are polynomials whose coefficients are zeroes and units. Prove that one of the polynomials

F

and

G

can be represented in the form

(1+x+x^2+...x^{k-1})T(x),

where

k>1

and

T

is a polynomial whose coefficients are zeroes and units.

Problem Statement